Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(299,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.18653618192\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 299.5 | ||
Character | \(\chi\) | \(=\) | 900.299 |
Dual form | 900.2.o.b.599.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.19709 | − | 0.752973i | −0.846473 | − | 0.532432i | ||||
\(3\) | 0.425108 | + | 1.67907i | 0.245436 | + | 0.969413i | ||||
\(4\) | 0.866065 | + | 1.80276i | 0.433032 | + | 0.901378i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.755401 | − | 2.33010i | 0.308391 | − | 0.951260i | ||||
\(7\) | 1.08216 | − | 1.87435i | 0.409018 | − | 0.708440i | −0.585762 | − | 0.810483i | \(-0.699205\pi\) |
0.994780 | + | 0.102043i | \(0.0325381\pi\) | |||||||
\(8\) | 0.320666 | − | 2.81019i | 0.113373 | − | 0.993553i | ||||
\(9\) | −2.63857 | + | 1.42758i | −0.879522 | + | 0.475858i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44632 | + | 2.50510i | −0.436083 | + | 0.755317i | −0.997383 | − | 0.0722948i | \(-0.976968\pi\) |
0.561301 | + | 0.827612i | \(0.310301\pi\) | |||||||
\(12\) | −2.65879 | + | 2.22055i | −0.767526 | + | 0.641018i | ||||
\(13\) | 5.72095 | − | 3.30299i | 1.58671 | − | 0.916085i | 0.592860 | − | 0.805306i | \(-0.297999\pi\) |
0.993845 | − | 0.110779i | \(-0.0353346\pi\) | |||||||
\(14\) | −2.70678 | + | 1.42894i | −0.723418 | + | 0.381901i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.49986 | + | 3.12261i | −0.624966 | + | 0.780652i | ||||
\(17\) | 5.08829 | 1.23409 | 0.617045 | − | 0.786928i | \(-0.288330\pi\) | ||||
0.617045 | + | 0.786928i | \(0.288330\pi\) | |||||||
\(18\) | 4.23353 | + | 0.277827i | 0.997854 | + | 0.0654844i | ||||
\(19\) | − | 4.66790i | − | 1.07089i | −0.844570 | − | 0.535445i | \(-0.820144\pi\) | ||
0.844570 | − | 0.535445i | \(-0.179856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.60721 | + | 1.02022i | 0.787158 | + | 0.222630i | ||||
\(22\) | 3.61766 | − | 1.90980i | 0.771287 | − | 0.407171i | ||||
\(23\) | −2.50662 | + | 1.44720i | −0.522666 | + | 0.301761i | −0.738025 | − | 0.674774i | \(-0.764241\pi\) |
0.215359 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(24\) | 4.85483 | − | 0.656214i | 0.990988 | − | 0.133949i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.33557 | − | 0.353728i | −1.83086 | − | 0.0693718i | ||||
\(27\) | −3.51868 | − | 3.82347i | −0.677170 | − | 0.735827i | ||||
\(28\) | 4.31623 | + | 0.327557i | 0.815690 | + | 0.0619025i | ||||
\(29\) | 5.99593 | + | 3.46175i | 1.11342 | + | 0.642831i | 0.939712 | − | 0.341967i | \(-0.111093\pi\) |
0.173704 | + | 0.984798i | \(0.444427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.51887 | − | 2.60897i | 0.811613 | − | 0.468585i | −0.0359024 | − | 0.999355i | \(-0.511431\pi\) |
0.847516 | + | 0.530770i | \(0.178097\pi\) | |||||||
\(32\) | 5.34381 | − | 1.85572i | 0.944661 | − | 0.328049i | ||||
\(33\) | −4.82109 | − | 1.36354i | −0.839245 | − | 0.237362i | ||||
\(34\) | −6.09115 | − | 3.83134i | −1.04462 | − | 0.657069i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.85874 | − | 3.52032i | −0.809790 | − | 0.586720i | ||||
\(37\) | − | 4.58347i | − | 0.753518i | −0.926311 | − | 0.376759i | \(-0.877038\pi\) | ||
0.926311 | − | 0.376759i | \(-0.122962\pi\) | |||||||
\(38\) | −3.51480 | + | 5.58792i | −0.570176 | + | 0.906480i | ||||
\(39\) | 7.97798 | + | 8.20175i | 1.27750 | + | 1.31333i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.18802 | + | 2.41795i | −0.654059 | + | 0.377621i | −0.790009 | − | 0.613095i | \(-0.789924\pi\) |
0.135951 | + | 0.990716i | \(0.456591\pi\) | |||||||
\(42\) | −3.54997 | − | 3.93743i | −0.547773 | − | 0.607559i | ||||
\(43\) | −2.20241 | + | 3.81468i | −0.335864 | + | 0.581733i | −0.983650 | − | 0.180089i | \(-0.942361\pi\) |
0.647787 | + | 0.761822i | \(0.275695\pi\) | |||||||
\(44\) | −5.76870 | − | 0.437785i | −0.869664 | − | 0.0659986i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.09035 | + | 0.154985i | 0.603089 | + | 0.0228513i | ||||
\(47\) | 0.0167877 | + | 0.00969237i | 0.00244874 | + | 0.00141378i | 0.501224 | − | 0.865318i | \(-0.332883\pi\) |
−0.498775 | + | 0.866731i | \(0.666217\pi\) | |||||||
\(48\) | −6.30580 | − | 2.87000i | −0.910163 | − | 0.414249i | ||||
\(49\) | 1.15786 | + | 2.00548i | 0.165409 | + | 0.286497i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.16307 | + | 8.54360i | 0.302891 | + | 1.19634i | ||||
\(52\) | 10.9092 | + | 7.45287i | 1.51283 | + | 1.03353i | ||||
\(53\) | 3.21239 | 0.441256 | 0.220628 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220628 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(54\) | 1.33322 | + | 7.22652i | 0.181428 | + | 0.983404i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.92028 | − | 3.64212i | −0.657501 | − | 0.486698i | ||||
\(57\) | 7.83775 | − | 1.98436i | 1.03813 | − | 0.262836i | ||||
\(58\) | −4.57108 | − | 8.65881i | −0.600212 | − | 1.13696i | ||||
\(59\) | 4.02651 | + | 6.97412i | 0.524207 | + | 0.907953i | 0.999603 | + | 0.0281811i | \(0.00897150\pi\) |
−0.475396 | + | 0.879772i | \(0.657695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.321400 | + | 0.556681i | −0.0411510 | + | 0.0712757i | −0.885867 | − | 0.463939i | \(-0.846436\pi\) |
0.844716 | + | 0.535214i | \(0.179769\pi\) | |||||||
\(62\) | −7.37400 | − | 0.279404i | −0.936499 | − | 0.0354843i | ||||
\(63\) | −0.179566 | + | 6.49047i | −0.0226232 | + | 0.817723i | ||||
\(64\) | −7.79435 | − | 1.80227i | −0.974293 | − | 0.225283i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.74459 | + | 5.26243i | 0.584019 | + | 0.647761i | ||||
\(67\) | 4.73363 | + | 8.19888i | 0.578304 | + | 1.00165i | 0.995674 | + | 0.0929158i | \(0.0296187\pi\) |
−0.417370 | + | 0.908737i | \(0.637048\pi\) | |||||||
\(68\) | 4.40678 | + | 9.17294i | 0.534401 | + | 1.11238i | ||||
\(69\) | −3.49553 | − | 3.59357i | −0.420812 | − | 0.432615i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.17635 | −0.139607 | −0.0698035 | − | 0.997561i | \(-0.522237\pi\) | ||||
−0.0698035 | + | 0.997561i | \(0.522237\pi\) | |||||||
\(72\) | 3.16566 | + | 7.87265i | 0.373077 | + | 0.927801i | ||||
\(73\) | 2.32539i | 0.272166i | 0.990697 | + | 0.136083i | \(0.0434514\pi\) | ||||
−0.990697 | + | 0.136083i | \(0.956549\pi\) | |||||||
\(74\) | −3.45123 | + | 5.48685i | −0.401197 | + | 0.637833i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.41509 | − | 4.04271i | 0.965278 | − | 0.463730i | ||||
\(77\) | 3.13030 | + | 5.42184i | 0.356731 | + | 0.617876i | ||||
\(78\) | −3.37469 | − | 15.8255i | −0.382109 | − | 1.79188i | ||||
\(79\) | 14.6983 | + | 8.48606i | 1.65369 | + | 0.954756i | 0.975538 | + | 0.219830i | \(0.0705503\pi\) |
0.678148 | + | 0.734926i | \(0.262783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.92406 | − | 7.53350i | 0.547118 | − | 0.837056i | ||||
\(82\) | 6.83410 | + | 0.258947i | 0.754700 | + | 0.0285959i | ||||
\(83\) | 1.64651 | + | 0.950613i | 0.180728 | + | 0.104343i | 0.587635 | − | 0.809126i | \(-0.300059\pi\) |
−0.406907 | + | 0.913470i | \(0.633393\pi\) | |||||||
\(84\) | 1.28487 | + | 7.38650i | 0.140191 | + | 0.805933i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.50883 | − | 2.90817i | 0.594033 | − | 0.313597i | ||||
\(87\) | −3.26361 | + | 11.5392i | −0.349896 | + | 1.23713i | ||||
\(88\) | 6.57603 | + | 4.86774i | 0.701007 | + | 0.518903i | ||||
\(89\) | 3.72649i | 0.395007i | 0.980302 | + | 0.197503i | \(0.0632834\pi\) | ||||
−0.980302 | + | 0.197503i | \(0.936717\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 14.2974i | − | 1.49878i | ||||||
\(92\) | −4.77983 | − | 3.26545i | −0.498332 | − | 0.340447i | ||||
\(93\) | 6.30166 | + | 6.47842i | 0.653452 | + | 0.671780i | ||||
\(94\) | −0.0127983 | − | 0.0242433i | −0.00132005 | − | 0.00250051i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.38759 | + | 8.18375i | 0.549869 | + | 0.835251i | ||||
\(97\) | −10.0127 | − | 5.78082i | −1.01663 | − | 0.586953i | −0.103506 | − | 0.994629i | \(-0.533006\pi\) |
−0.913127 | + | 0.407675i | \(0.866339\pi\) | |||||||
\(98\) | 0.123999 | − | 3.27258i | 0.0125258 | − | 0.330581i | ||||
\(99\) | 0.239992 | − | 8.67461i | 0.0241201 | − | 0.871831i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.46327 | − | 5.46362i | −0.941630 | − | 0.543650i | −0.0511591 | − | 0.998691i | \(-0.516292\pi\) |
−0.890471 | + | 0.455040i | \(0.849625\pi\) | |||||||
\(102\) | 3.84369 | − | 11.8562i | 0.380582 | − | 1.17394i | ||||
\(103\) | −0.317664 | − | 0.550211i | −0.0313004 | − | 0.0542139i | 0.849951 | − | 0.526862i | \(-0.176632\pi\) |
−0.881251 | + | 0.472648i | \(0.843298\pi\) | |||||||
\(104\) | −7.44752 | − | 17.1361i | −0.730289 | − | 1.68033i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.84553 | − | 2.41884i | −0.373511 | − | 0.234939i | ||||
\(107\) | − | 18.8050i | − | 1.81795i | −0.416850 | − | 0.908975i | \(-0.636866\pi\) | ||
0.416850 | − | 0.908975i | \(-0.363134\pi\) | |||||||
\(108\) | 3.84538 | − | 9.65469i | 0.370022 | − | 0.929023i | ||||
\(109\) | 3.39053 | 0.324754 | 0.162377 | − | 0.986729i | \(-0.448084\pi\) | ||||
0.162377 | + | 0.986729i | \(0.448084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.69598 | − | 1.94847i | 0.730470 | − | 0.184941i | ||||
\(112\) | 3.14763 | + | 8.06479i | 0.297423 | + | 0.762051i | ||||
\(113\) | −0.499103 | − | 0.864471i | −0.0469516 | − | 0.0813226i | 0.841595 | − | 0.540110i | \(-0.181617\pi\) |
−0.888546 | + | 0.458787i | \(0.848284\pi\) | |||||||
\(114\) | −10.8767 | − | 3.52614i | −1.01869 | − | 0.330253i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.04783 | + | 13.8073i | −0.0972888 | + | 1.28198i | ||||
\(117\) | −10.3798 | + | 16.8822i | −0.959615 | + | 1.56076i | ||||
\(118\) | 0.431213 | − | 11.3805i | 0.0396963 | − | 1.04766i | ||||
\(119\) | 5.50634 | − | 9.53725i | 0.504765 | − | 0.874279i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.31630 | + | 2.27991i | 0.119664 | + | 0.207264i | ||||
\(122\) | 0.803911 | − | 0.424394i | 0.0727827 | − | 0.0384228i | ||||
\(123\) | −5.84028 | − | 6.00409i | −0.526600 | − | 0.541371i | ||||
\(124\) | 8.61698 | + | 5.88689i | 0.773828 | + | 0.528658i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.10210 | − | 7.63449i | 0.454532 | − | 0.680135i | ||||
\(127\) | 8.78450 | 0.779498 | 0.389749 | − | 0.920921i | \(-0.372562\pi\) | ||||
0.389749 | + | 0.920921i | \(0.372562\pi\) | |||||||
\(128\) | 7.97350 | + | 8.02641i | 0.704765 | + | 0.709441i | ||||
\(129\) | −7.34138 | − | 2.07635i | −0.646372 | − | 0.182812i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.06346 | − | 12.2343i | −0.617137 | − | 1.06891i | −0.990005 | − | 0.141029i | \(-0.954959\pi\) |
0.372868 | − | 0.927884i | \(-0.378374\pi\) | |||||||
\(132\) | −1.71725 | − | 9.87217i | −0.149467 | − | 0.859262i | ||||
\(133\) | −8.74931 | − | 5.05142i | −0.758661 | − | 0.438013i | ||||
\(134\) | 0.506940 | − | 13.3791i | 0.0437929 | − | 1.15578i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.63164 | − | 14.2991i | 0.139912 | − | 1.22613i | ||||
\(137\) | 7.60127 | − | 13.1658i | 0.649420 | − | 1.12483i | −0.333841 | − | 0.942629i | \(-0.608345\pi\) |
0.983262 | − | 0.182200i | \(-0.0583217\pi\) | |||||||
\(138\) | 1.47861 | + | 6.93388i | 0.125868 | + | 0.590251i | ||||
\(139\) | −2.20036 | + | 1.27038i | −0.186632 | + | 0.107752i | −0.590405 | − | 0.807107i | \(-0.701032\pi\) |
0.403773 | + | 0.914859i | \(0.367699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.00913761 | + | 0.0323080i | −0.000769525 | + | 0.00272083i | ||||
\(142\) | 1.40820 | + | 0.885759i | 0.118174 | + | 0.0743312i | ||||
\(143\) | 19.1087i | 1.59795i | ||||||||
\(144\) | 2.13830 | − | 11.8080i | 0.178191 | − | 0.983996i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.75095 | − | 2.78371i | 0.144910 | − | 0.230381i | ||||
\(147\) | −2.87512 | + | 2.79668i | −0.237136 | + | 0.230666i | ||||
\(148\) | 8.26289 | − | 3.96959i | 0.679205 | − | 0.326298i | ||||
\(149\) | −5.98481 | + | 3.45533i | −0.490294 | + | 0.283072i | −0.724697 | − | 0.689068i | \(-0.758020\pi\) |
0.234402 | + | 0.972140i | \(0.424687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4571 | + | 10.6562i | 1.50202 | + | 0.867191i | 0.999997 | + | 0.00233576i | \(0.000743497\pi\) |
0.502021 | + | 0.864855i | \(0.332590\pi\) | |||||||
\(152\) | −13.1177 | − | 1.49684i | −1.06399 | − | 0.121410i | ||||
\(153\) | −13.4258 | + | 7.26391i | −1.08541 | + | 0.587252i | ||||
\(154\) | 0.335235 | − | 8.84748i | 0.0270140 | − | 0.712950i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.87632 | + | 21.4856i | −0.630610 | + | 1.72023i | ||||
\(157\) | −10.1062 | + | 5.83484i | −0.806566 | + | 0.465671i | −0.845762 | − | 0.533560i | \(-0.820854\pi\) |
0.0391957 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(158\) | −11.2054 | − | 21.2260i | −0.891457 | − | 1.68865i | ||||
\(159\) | 1.36561 | + | 5.39384i | 0.108300 | + | 0.427759i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.26438i | 0.493703i | ||||||||
\(162\) | −11.5671 | + | 5.31062i | −0.908795 | + | 0.417242i | ||||
\(163\) | 0.438006 | 0.0343073 | 0.0171536 | − | 0.999853i | \(-0.494540\pi\) | ||||
0.0171536 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(164\) | −7.98608 | − | 5.45587i | −0.623608 | − | 0.426032i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.25524 | − | 2.37775i | −0.0974256 | − | 0.184549i | ||||
\(167\) | 3.60751 | − | 2.08280i | 0.279157 | − | 0.161172i | −0.353884 | − | 0.935289i | \(-0.615139\pi\) |
0.633042 | + | 0.774118i | \(0.281806\pi\) | |||||||
\(168\) | 4.02372 | − | 9.80980i | 0.310437 | − | 0.756843i | ||||
\(169\) | 15.3195 | − | 26.5341i | 1.17842 | − | 2.04109i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.66378 | + | 12.3166i | 0.509592 | + | 0.941872i | ||||
\(172\) | −8.78436 | − | 0.666643i | −0.669801 | − | 0.0508311i | ||||
\(173\) | −4.47638 | + | 7.75332i | −0.340333 | + | 0.589474i | −0.984494 | − | 0.175416i | \(-0.943873\pi\) |
0.644162 | + | 0.764889i | \(0.277206\pi\) | |||||||
\(174\) | 12.5956 | − | 11.3561i | 0.954866 | − | 0.860904i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.20685 | − | 10.7787i | −0.317103 | − | 0.812476i | ||||
\(177\) | −9.99835 | + | 9.72556i | −0.751522 | + | 0.731018i | ||||
\(178\) | 2.80594 | − | 4.46095i | 0.210314 | − | 0.334363i | ||||
\(179\) | −10.5263 | −0.786776 | −0.393388 | − | 0.919373i | \(-0.628697\pi\) | ||||
−0.393388 | + | 0.919373i | \(0.628697\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.50854 | −0.706765 | −0.353382 | − | 0.935479i | \(-0.614968\pi\) | ||||
−0.353382 | + | 0.935479i | \(0.614968\pi\) | |||||||
\(182\) | −10.7656 | + | 17.1154i | −0.797998 | + | 1.26868i | ||||
\(183\) | −1.07134 | − | 0.303004i | −0.0791955 | − | 0.0223987i | ||||
\(184\) | 3.26311 | + | 7.50814i | 0.240560 | + | 0.553507i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.66561 | − | 12.5002i | −0.195452 | − | 0.916563i | ||||
\(187\) | −7.35930 | + | 12.7467i | −0.538165 | + | 0.932130i | ||||
\(188\) | −0.00293377 | + | 0.0386583i | −0.000213967 | + | 0.00281945i | ||||
\(189\) | −10.9743 | + | 2.45765i | −0.798263 | + | 0.178768i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.08040 | + | 10.5316i | −0.439963 | + | 0.762038i | −0.997686 | − | 0.0679893i | \(-0.978342\pi\) |
0.557723 | + | 0.830027i | \(0.311675\pi\) | |||||||
\(192\) | −0.287309 | − | 13.8534i | −0.0207347 | − | 0.999785i | ||||
\(193\) | −12.1493 | + | 7.01439i | −0.874525 | + | 0.504907i | −0.868849 | − | 0.495077i | \(-0.835140\pi\) |
−0.00567551 | + | 0.999984i | \(0.501807\pi\) | |||||||
\(194\) | 7.63331 | + | 14.4595i | 0.548040 | + | 1.03813i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.61260 | + | 3.82422i | −0.186614 | + | 0.273158i | ||||
\(197\) | 7.21555 | 0.514086 | 0.257043 | − | 0.966400i | \(-0.417252\pi\) | ||||
0.257043 | + | 0.966400i | \(0.417252\pi\) | |||||||
\(198\) | −6.81904 | + | 10.2036i | −0.484608 | + | 0.725139i | ||||
\(199\) | − | 8.63093i | − | 0.611830i | −0.952059 | − | 0.305915i | \(-0.901038\pi\) | ||
0.952059 | − | 0.305915i | \(-0.0989624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.7542 | + | 11.4335i | −0.829078 | + | 0.806458i | ||||
\(202\) | 7.21446 | + | 13.6660i | 0.507607 | + | 0.961539i | ||||
\(203\) | 12.9771 | − | 7.49233i | 0.910814 | − | 0.525858i | ||||
\(204\) | −13.5287 | + | 11.2988i | −0.947196 | + | 0.791074i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.0340198 | + | 0.897846i | −0.00237027 | + | 0.0625559i | ||||
\(207\) | 4.54789 | − | 7.39690i | 0.316100 | − | 0.514120i | ||||
\(208\) | −3.98764 | + | 26.1213i | −0.276493 | + | 1.81119i | ||||
\(209\) | 11.6936 | + | 6.75129i | 0.808862 | + | 0.466997i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1103 | + | 9.30130i | −1.10908 | + | 0.640328i | −0.938591 | − | 0.345031i | \(-0.887868\pi\) |
−0.170490 | + | 0.985359i | \(0.554535\pi\) | |||||||
\(212\) | 2.78214 | + | 5.79116i | 0.191078 | + | 0.397739i | ||||
\(213\) | −0.500076 | − | 1.97518i | −0.0342647 | − | 0.135337i | ||||
\(214\) | −14.1597 | + | 22.5114i | −0.967935 | + | 1.53885i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −11.8730 | + | 8.66210i | −0.807855 | + | 0.589381i | ||||
\(217\) | − | 11.2933i | − | 0.766639i | ||||||
\(218\) | −4.05878 | − | 2.55298i | −0.274895 | − | 0.172909i | ||||
\(219\) | −3.90450 | + | 0.988543i | −0.263841 | + | 0.0667995i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.1098 | − | 16.8066i | 1.95814 | − | 1.13053i | ||||
\(222\) | −10.6800 | − | 3.46236i | −0.716792 | − | 0.232378i | ||||
\(223\) | −6.17187 | + | 10.6900i | −0.413299 | + | 0.715854i | −0.995248 | − | 0.0973706i | \(-0.968957\pi\) |
0.581949 | + | 0.813225i | \(0.302290\pi\) | |||||||
\(224\) | 2.30457 | − | 12.0244i | 0.153980 | − | 0.803413i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0534506 | + | 1.41066i | −0.00355548 | + | 0.0938359i | ||||
\(227\) | 0.644365 | + | 0.372024i | 0.0427680 | + | 0.0246921i | 0.521232 | − | 0.853415i | \(-0.325473\pi\) |
−0.478464 | + | 0.878107i | \(0.658806\pi\) | |||||||
\(228\) | 10.3653 | + | 12.4110i | 0.686460 | + | 0.821936i | ||||
\(229\) | −13.0783 | − | 22.6523i | −0.864238 | − | 1.49690i | −0.867801 | − | 0.496911i | \(-0.834468\pi\) |
0.00356308 | − | 0.999994i | \(-0.498866\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.77295 | + | 7.56087i | −0.511422 | + | 0.497469i | ||||
\(232\) | 11.6509 | − | 15.7396i | 0.764917 | − | 1.03336i | ||||
\(233\) | 25.8264 | 1.69195 | 0.845973 | − | 0.533226i | \(-0.179021\pi\) | ||||
0.845973 | + | 0.533226i | \(0.179021\pi\) | |||||||
\(234\) | 25.1375 | − | 12.3939i | 1.64329 | − | 0.810214i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.08542 | + | 13.2989i | −0.591411 | + | 0.865682i | ||||
\(237\) | −8.00034 | + | 28.2870i | −0.519678 | + | 1.83744i | ||||
\(238\) | −13.7729 | + | 7.27086i | −0.892764 | + | 0.471300i | ||||
\(239\) | −4.11600 | − | 7.12913i | −0.266242 | − | 0.461145i | 0.701646 | − | 0.712526i | \(-0.252449\pi\) |
−0.967888 | + | 0.251381i | \(0.919115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0705544 | − | 0.122204i | 0.00454481 | − | 0.00787184i | −0.863744 | − | 0.503931i | \(-0.831887\pi\) |
0.868289 | + | 0.496059i | \(0.165220\pi\) | |||||||
\(242\) | 0.140967 | − | 3.72040i | 0.00906173 | − | 0.239156i | ||||
\(243\) | 14.7426 | + | 5.06529i | 0.945735 | + | 0.324939i | ||||
\(244\) | −1.28191 | − | 0.0972841i | −0.0820661 | − | 0.00622797i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.47044 | + | 11.5850i | 0.157510 | + | 0.738634i | ||||
\(247\) | −15.4180 | − | 26.7048i | −0.981026 | − | 1.69919i | ||||
\(248\) | −5.88266 | − | 13.5355i | −0.373549 | − | 0.859505i | ||||
\(249\) | −0.896202 | + | 3.16872i | −0.0567945 | + | 0.200810i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.50499 | −0.599950 | −0.299975 | − | 0.953947i | \(-0.596978\pi\) | ||||
−0.299975 | + | 0.953947i | \(0.596978\pi\) | |||||||
\(252\) | −11.8563 | + | 5.29746i | −0.746874 | + | 0.333708i | ||||
\(253\) | − | 8.37244i | − | 0.526371i | ||||||
\(254\) | −10.5159 | − | 6.61449i | −0.659824 | − | 0.415030i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.50136 | − | 15.6122i | −0.218835 | − | 0.975762i | ||||
\(257\) | −12.9923 | − | 22.5033i | −0.810436 | − | 1.40372i | −0.912559 | − | 0.408945i | \(-0.865897\pi\) |
0.102123 | − | 0.994772i | \(-0.467436\pi\) | |||||||
\(258\) | 7.22489 | + | 8.01344i | 0.449802 | + | 0.498895i | ||||
\(259\) | −8.59106 | − | 4.96005i | −0.533822 | − | 0.308202i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.7626 | − | 0.574418i | −1.28517 | − | 0.0355556i | ||||
\(262\) | −0.756450 | + | 19.9642i | −0.0467336 | + | 1.23339i | ||||
\(263\) | −23.2758 | − | 13.4383i | −1.43525 | − | 0.828640i | −0.437732 | − | 0.899105i | \(-0.644218\pi\) |
−0.997514 | + | 0.0704654i | \(0.977552\pi\) | |||||||
\(264\) | −5.37776 | + | 13.1110i | −0.330979 | + | 0.806923i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.67016 | + | 12.6350i | 0.408974 | + | 0.774702i | ||||
\(267\) | −6.25704 | + | 1.58416i | −0.382925 | + | 0.0969491i | ||||
\(268\) | −10.6810 | + | 15.6343i | −0.652443 | + | 0.955019i | ||||
\(269\) | 16.4030i | 1.00011i | 0.865995 | + | 0.500053i | \(0.166686\pi\) | ||||
−0.865995 | + | 0.500053i | \(0.833314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.0484i | − | 0.974873i | −0.873158 | − | 0.487437i | \(-0.837932\pi\) | ||
0.873158 | − | 0.487437i | \(-0.162068\pi\) | |||||||
\(272\) | −12.7200 | + | 15.8887i | −0.771264 | + | 0.963395i | ||||
\(273\) | 24.0064 | − | 6.07796i | 1.45294 | − | 0.367855i | ||||
\(274\) | −19.0129 | + | 10.0371i | −1.14861 | + | 0.606365i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.45098 | − | 9.41386i | 0.207725 | − | 0.566647i | ||||
\(277\) | −21.0720 | − | 12.1659i | −1.26609 | − | 0.730978i | −0.291845 | − | 0.956466i | \(-0.594269\pi\) |
−0.974246 | + | 0.225488i | \(0.927602\pi\) | |||||||
\(278\) | 3.59060 | + | 0.136049i | 0.215350 | + | 0.00815969i | ||||
\(279\) | −8.19884 | + | 13.3350i | −0.490852 | + | 0.798344i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.04166 | + | 5.22020i | 0.539380 | + | 0.311411i | 0.744828 | − | 0.667257i | \(-0.232532\pi\) |
−0.205448 | + | 0.978668i | \(0.565865\pi\) | |||||||
\(282\) | 0.0352656 | − | 0.0317954i | 0.00210004 | − | 0.00189339i | ||||
\(283\) | −7.44455 | − | 12.8943i | −0.442533 | − | 0.766489i | 0.555344 | − | 0.831621i | \(-0.312587\pi\) |
−0.997877 | + | 0.0651317i | \(0.979253\pi\) | |||||||
\(284\) | −1.01880 | − | 2.12067i | −0.0604544 | − | 0.125839i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.3884 | − | 22.8750i | 0.850802 | − | 1.35262i | ||||
\(287\) | 10.4664i | 0.617815i | ||||||||
\(288\) | −11.4508 | + | 12.5251i | −0.674745 | + | 0.738051i | ||||
\(289\) | 8.89065 | 0.522979 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.44994 | − | 19.2695i | 0.319481 | − | 1.12960i | ||||
\(292\) | −4.19211 | + | 2.01394i | −0.245325 | + | 0.117857i | ||||
\(293\) | −13.0589 | − | 22.6187i | −0.762911 | − | 1.32140i | −0.941344 | − | 0.337449i | \(-0.890436\pi\) |
0.178433 | − | 0.983952i | \(-0.442897\pi\) | |||||||
\(294\) | 5.54761 | − | 1.18300i | 0.323543 | − | 0.0689938i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.8804 | − | 1.46976i | −0.748660 | − | 0.0854283i | ||||
\(297\) | 14.6673 | − | 3.28469i | 0.851084 | − | 0.190597i | ||||
\(298\) | 9.76614 | + | 0.370043i | 0.565737 | + | 0.0214360i | ||||
\(299\) | −9.56014 | + | 16.5587i | −0.552877 | + | 0.957612i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.76671 | + | 8.25618i | 0.274748 | + | 0.475878i | ||||
\(302\) | −14.0710 | − | 26.6542i | −0.809698 | − | 1.53378i | ||||
\(303\) | 5.15090 | − | 18.2121i | 0.295911 | − | 1.04626i | ||||
\(304\) | 14.5760 | + | 11.6691i | 0.835993 | + | 0.669270i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 21.5414 | + | 1.41366i | 1.23144 | + | 0.0808137i | ||||
\(307\) | 28.5542 | 1.62967 | 0.814837 | − | 0.579690i | \(-0.196826\pi\) | ||||
0.814837 | + | 0.579690i | \(0.196826\pi\) | |||||||
\(308\) | −7.06322 | + | 10.3388i | −0.402464 | + | 0.589110i | ||||
\(309\) | 0.788802 | − | 0.767281i | 0.0448734 | − | 0.0436491i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0440224 | + | 0.0762490i | 0.00249628 | + | 0.00432369i | 0.867271 | − | 0.497837i | \(-0.165872\pi\) |
−0.864775 | + | 0.502160i | \(0.832539\pi\) | |||||||
\(312\) | 25.6068 | − | 19.7896i | 1.44970 | − | 1.12037i | ||||
\(313\) | −13.1775 | − | 7.60804i | −0.744837 | − | 0.430032i | 0.0789885 | − | 0.996876i | \(-0.474831\pi\) |
−0.823825 | + | 0.566844i | \(0.808164\pi\) | |||||||
\(314\) | 16.4916 | + | 0.624873i | 0.930675 | + | 0.0352636i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.56863 | + | 33.8469i | −0.144497 | + | 1.90404i | ||||
\(317\) | 3.58277 | − | 6.20554i | 0.201228 | − | 0.348538i | −0.747696 | − | 0.664041i | \(-0.768840\pi\) |
0.948925 | + | 0.315503i | \(0.102173\pi\) | |||||||
\(318\) | 2.42664 | − | 7.48520i | 0.136079 | − | 0.419749i | ||||
\(319\) | −17.3441 | + | 10.0136i | −0.971082 | + | 0.560655i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.5750 | − | 7.99417i | 1.76234 | − | 0.446191i | ||||
\(322\) | 4.71691 | − | 7.49905i | 0.262863 | − | 0.417906i | ||||
\(323\) | − | 23.7516i | − | 1.32158i | ||||||
\(324\) | 17.8456 | + | 2.35238i | 0.991424 | + | 0.130688i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.524334 | − | 0.329807i | −0.0290402 | − | 0.0182663i | ||||
\(327\) | 1.44134 | + | 5.69295i | 0.0797065 | + | 0.314821i | ||||
\(328\) | 5.45196 | + | 12.5445i | 0.301034 | + | 0.692653i | ||||
\(329\) | 0.0363339 | − | 0.0209774i | 0.00200315 | − | 0.00115652i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.709837 | − | 0.409824i | −0.0390161 | − | 0.0225260i | 0.480365 | − | 0.877069i | \(-0.340504\pi\) |
−0.519381 | + | 0.854543i | \(0.673838\pi\) | |||||||
\(332\) | −0.287740 | + | 3.79155i | −0.0157918 | + | 0.208088i | ||||
\(333\) | 6.54325 | + | 12.0938i | 0.358568 | + | 0.662736i | ||||
\(334\) | −5.88681 | − | 0.223054i | −0.322112 | − | 0.0122050i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.2033 | + | 8.71350i | −0.665744 | + | 0.475360i | ||||
\(337\) | 2.65680 | − | 1.53390i | 0.144725 | − | 0.0835571i | −0.425889 | − | 0.904775i | \(-0.640039\pi\) |
0.570614 | + | 0.821218i | \(0.306705\pi\) | |||||||
\(338\) | −38.3183 | + | 20.2287i | −2.08424 | + | 1.10029i | ||||
\(339\) | 1.23934 | − | 1.20552i | 0.0673115 | − | 0.0654750i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0937i | 0.817367i | ||||||||
\(342\) | 1.29687 | − | 19.7617i | 0.0701266 | − | 1.06859i | ||||
\(343\) | 20.1622 | 1.08866 | ||||||||
\(344\) | 10.0137 | + | 7.41242i | 0.539904 | + | 0.399651i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.1967 | − | 5.91085i | 0.601937 | − | 0.317769i | ||||
\(347\) | −19.3234 | + | 11.1564i | −1.03734 | + | 0.598906i | −0.919078 | − | 0.394077i | \(-0.871064\pi\) |
−0.118258 | + | 0.992983i | \(0.537731\pi\) | |||||||
\(348\) | −23.6289 | + | 4.11021i | −1.26664 | + | 0.220330i | ||||
\(349\) | −5.01965 | + | 8.69429i | −0.268696 | + | 0.465395i | −0.968525 | − | 0.248915i | \(-0.919926\pi\) |
0.699829 | + | 0.714310i | \(0.253259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.7590 | − | 10.2517i | −1.74855 | − | 0.547195i | ||||
\(352\) | −3.08009 | + | 16.0708i | −0.164169 | + | 0.856575i | ||||
\(353\) | 6.36616 | − | 11.0265i | 0.338836 | − | 0.586882i | −0.645378 | − | 0.763864i | \(-0.723300\pi\) |
0.984214 | + | 0.176982i | \(0.0566334\pi\) | |||||||
\(354\) | 19.2920 | − | 4.11392i | 1.02536 | − | 0.218652i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.71795 | + | 3.22738i | −0.356051 | + | 0.171051i | ||||
\(357\) | 18.3545 | + | 5.19117i | 0.971424 | + | 0.274746i | ||||
\(358\) | 12.6010 | + | 7.92605i | 0.665984 | + | 0.418905i | ||||
\(359\) | 5.93304 | 0.313134 | 0.156567 | − | 0.987667i | \(-0.449957\pi\) | ||||
0.156567 | + | 0.987667i | \(0.449957\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.78932 | −0.146806 | ||||||||
\(362\) | 11.3826 | + | 7.15967i | 0.598257 | + | 0.376304i | ||||
\(363\) | −3.26855 | + | 3.17938i | −0.171555 | + | 0.166874i | ||||
\(364\) | 25.7748 | − | 12.3825i | 1.35097 | − | 0.649020i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.05434 | + | 1.16941i | 0.0551111 | + | 0.0611261i | ||||
\(367\) | −13.3004 | + | 23.0370i | −0.694277 | + | 1.20252i | 0.276147 | + | 0.961115i | \(0.410942\pi\) |
−0.970424 | + | 0.241407i | \(0.922391\pi\) | |||||||
\(368\) | 1.74717 | − | 11.4450i | 0.0910777 | − | 0.596610i | ||||
\(369\) | 7.59855 | − | 12.3586i | 0.395565 | − | 0.643365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.47632 | − | 6.02116i | 0.180482 | − | 0.312603i | ||||
\(372\) | −6.22136 | + | 16.9711i | −0.322563 | + | 0.879910i | ||||
\(373\) | −22.9141 | + | 13.2294i | −1.18645 | + | 0.684995i | −0.957497 | − | 0.288444i | \(-0.906862\pi\) |
−0.228949 | + | 0.973438i | \(0.573529\pi\) | |||||||
\(374\) | 18.4077 | − | 9.71762i | 0.951838 | − | 0.502486i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0326207 | − | 0.0440686i | 0.00168228 | − | 0.00227266i | ||||
\(377\) | 45.7365 | 2.35555 | ||||||||
\(378\) | 14.9878 | + | 5.32131i | 0.770890 | + | 0.273699i | ||||
\(379\) | − | 21.3357i | − | 1.09594i | −0.836497 | − | 0.547972i | \(-0.815400\pi\) | ||
0.836497 | − | 0.547972i | \(-0.184600\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.73436 | + | 14.7498i | 0.191317 | + | 0.755655i | ||||
\(382\) | 15.2088 | − | 8.02889i | 0.778150 | − | 0.410794i | ||||
\(383\) | −2.73103 | + | 1.57676i | −0.139549 | + | 0.0805688i | −0.568149 | − | 0.822926i | \(-0.692340\pi\) |
0.428600 | + | 0.903494i | \(0.359007\pi\) | |||||||
\(384\) | −10.0873 | + | 16.8002i | −0.514766 | + | 0.857331i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.8255 | + | 0.751195i | 1.00909 | + | 0.0382348i | ||||
\(387\) | 0.365451 | − | 13.2094i | 0.0185769 | − | 0.671470i | ||||
\(388\) | 1.74979 | − | 23.0570i | 0.0888321 | − | 1.17054i | ||||
\(389\) | −12.9948 | − | 7.50253i | −0.658860 | − | 0.380393i | 0.132982 | − | 0.991118i | \(-0.457545\pi\) |
−0.791843 | + | 0.610725i | \(0.790878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7544 | + | 7.36374i | −0.645017 | + | 0.372400i | ||||
\(392\) | 6.00706 | − | 2.61073i | 0.303402 | − | 0.131862i | ||||
\(393\) | 17.5395 | − | 17.0610i | 0.884750 | − | 0.860611i | ||||
\(394\) | −8.63768 | − | 5.43311i | −0.435160 | − | 0.273716i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.8461 | − | 7.08013i | 0.796295 | − | 0.355790i | ||||
\(397\) | 10.0474i | 0.504266i | 0.967693 | + | 0.252133i | \(0.0811320\pi\) | ||||
−0.967693 | + | 0.252133i | \(0.918868\pi\) | |||||||
\(398\) | −6.49885 | + | 10.3320i | −0.325758 | + | 0.517898i | ||||
\(399\) | 4.76229 | − | 16.8381i | 0.238412 | − | 0.842960i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.85153 | + | 3.95573i | −0.342149 | + | 0.197540i | −0.661222 | − | 0.750190i | \(-0.729962\pi\) |
0.319073 | + | 0.947730i | \(0.396629\pi\) | |||||||
\(402\) | 22.6800 | − | 4.83639i | 1.13118 | − | 0.241217i | ||||
\(403\) | 17.2348 | − | 29.8516i | 0.858527 | − | 1.48701i | ||||
\(404\) | 1.65378 | − | 21.7918i | 0.0822784 | − | 1.08418i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −21.1763 | − | 0.802379i | −1.05096 | − | 0.0398214i | ||||
\(407\) | 11.4821 | + | 6.62918i | 0.569145 | + | 0.328596i | ||||
\(408\) | 24.7028 | − | 3.33901i | 1.22297 | − | 0.165305i | ||||
\(409\) | 13.5824 | + | 23.5255i | 0.671608 | + | 1.16326i | 0.977448 | + | 0.211177i | \(0.0677295\pi\) |
−0.305840 | + | 0.952083i | \(0.598937\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.3377 | + | 7.16619i | 1.24981 | + | 0.353482i | ||||
\(412\) | 0.716778 | − | 1.04919i | 0.0353131 | − | 0.0516899i | ||||
\(413\) | 17.4293 | 0.857640 | ||||||||
\(414\) | −11.0139 | + | 5.43035i | −0.541304 | + | 0.266887i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.4422 | − | 28.2670i | 1.19838 | − | 1.38591i | ||||
\(417\) | −3.06845 | − | 3.15452i | −0.150263 | − | 0.154477i | ||||
\(418\) | −8.91477 | − | 16.8869i | −0.436036 | − | 0.825964i | ||||
\(419\) | −4.28527 | − | 7.42230i | −0.209349 | − | 0.362603i | 0.742161 | − | 0.670222i | \(-0.233801\pi\) |
−0.951510 | + | 0.307619i | \(0.900468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.41504 | − | 5.91502i | 0.166439 | − | 0.288280i | −0.770727 | − | 0.637166i | \(-0.780107\pi\) |
0.937165 | + | 0.348886i | \(0.113440\pi\) | |||||||
\(422\) | 26.2892 | + | 0.996108i | 1.27974 | + | 0.0484898i | ||||
\(423\) | −0.0581320 | − | 0.00160828i | −0.00282647 | − | 7.81974e-5i | ||||
\(424\) | 1.03010 | − | 9.02743i | 0.0500263 | − | 0.438411i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.888615 | + | 2.74101i | −0.0430536 | + | 0.132803i | ||||
\(427\) | 0.695612 | + | 1.20483i | 0.0336630 | + | 0.0583060i | ||||
\(428\) | 33.9009 | − | 16.2864i | 1.63866 | − | 0.787231i | ||||
\(429\) | −32.0850 | + | 8.12329i | −1.54908 | + | 0.392196i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.5552 | 1.27912 | 0.639559 | − | 0.768742i | \(-0.279117\pi\) | ||||
0.639559 | + | 0.768742i | \(0.279117\pi\) | |||||||
\(432\) | 20.7354 | − | 1.42930i | 0.997633 | − | 0.0687674i | ||||
\(433\) | − | 12.4714i | − | 0.599339i | −0.954043 | − | 0.299669i | \(-0.903124\pi\) | ||
0.954043 | − | 0.299669i | \(-0.0968763\pi\) | |||||||
\(434\) | −8.50354 | + | 13.5191i | −0.408183 | + | 0.648939i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.93642 | + | 6.11230i | 0.140629 | + | 0.292726i | ||||
\(437\) | 6.75537 | + | 11.7006i | 0.323153 | + | 0.559718i | ||||
\(438\) | 5.41839 | + | 1.75660i | 0.258901 | + | 0.0839337i | ||||
\(439\) | −12.8412 | − | 7.41389i | −0.612879 | − | 0.353846i | 0.161212 | − | 0.986920i | \(-0.448460\pi\) |
−0.774091 | + | 0.633074i | \(0.781793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.91806 | − | 3.63865i | −0.281813 | − | 0.173269i | ||||
\(442\) | −47.5020 | − | 1.79987i | −2.25944 | − | 0.0856111i | ||||
\(443\) | 34.2297 | + | 19.7625i | 1.62630 | + | 0.938945i | 0.985184 | + | 0.171501i | \(0.0548618\pi\) |
0.641117 | + | 0.767444i | \(0.278472\pi\) | |||||||
\(444\) | 10.1778 | + | 12.1865i | 0.483019 | + | 0.578345i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 15.4376 | − | 8.14966i | 0.730990 | − | 0.385898i | ||||
\(447\) | −8.34594 | − | 8.58003i | −0.394749 | − | 0.405822i | ||||
\(448\) | −11.8128 | + | 12.6590i | −0.558103 | + | 0.598083i | ||||
\(449\) | 22.8395i | 1.07786i | 0.842349 | + | 0.538932i | \(0.181172\pi\) | ||||
−0.842349 | + | 0.538932i | \(0.818828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.9886i | − | 0.658695i | ||||||
\(452\) | 1.12618 | − | 1.64845i | 0.0529709 | − | 0.0775365i | ||||
\(453\) | −10.0463 | + | 35.5209i | −0.472016 | + | 1.66892i | ||||
\(454\) | −0.491241 | − | 0.930537i | −0.0230551 | − | 0.0436723i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.06315 | − | 22.6619i | −0.143445 | − | 1.06124i | ||||
\(457\) | 0.720950 | + | 0.416241i | 0.0337246 | + | 0.0194709i | 0.516768 | − | 0.856126i | \(-0.327135\pi\) |
−0.483043 | + | 0.875597i | \(0.660468\pi\) | |||||||
\(458\) | −1.40060 | + | 36.9645i | −0.0654457 | + | 1.72724i | ||||
\(459\) | −17.9040 | − | 19.4549i | −0.835689 | − | 0.908077i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.9887 | − | 17.8913i | −1.44329 | − | 0.833281i | −0.445218 | − | 0.895422i | \(-0.646874\pi\) |
−0.998067 | + | 0.0621408i | \(0.980207\pi\) | |||||||
\(462\) | 14.9981 | − | 3.19826i | 0.697773 | − | 0.148796i | ||||
\(463\) | 4.16373 | + | 7.21179i | 0.193505 | + | 0.335160i | 0.946409 | − | 0.322969i | \(-0.104681\pi\) |
−0.752904 | + | 0.658130i | \(0.771348\pi\) | |||||||
\(464\) | −25.7987 | + | 10.0690i | −1.19767 | + | 0.467443i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −30.9166 | − | 19.4466i | −1.43219 | − | 0.900846i | ||||
\(467\) | 16.8607i | 0.780220i | 0.920768 | + | 0.390110i | \(0.127563\pi\) | ||||
−0.920768 | + | 0.390110i | \(0.872437\pi\) | |||||||
\(468\) | −39.4242 | − | 4.09119i | −1.82238 | − | 0.189115i | ||||
\(469\) | 20.4901 | 0.946147 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.0934 | − | 14.4887i | −0.649388 | − | 0.667603i | ||||
\(472\) | 20.8898 | − | 9.07890i | 0.961530 | − | 0.417890i | ||||
\(473\) | −6.37077 | − | 11.0345i | −0.292929 | − | 0.507367i | ||||
\(474\) | 30.8765 | − | 27.8381i | 1.41820 | − | 1.27865i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.9622 | + | 1.66671i | 1.00664 | + | 0.0763933i | ||||
\(477\) | −8.47611 | + | 4.58593i | −0.388094 | + | 0.209975i | ||||
\(478\) | −0.440797 | + | 11.6335i | −0.0201616 | + | 0.532102i | ||||
\(479\) | 2.64691 | − | 4.58458i | 0.120940 | − | 0.209475i | −0.799198 | − | 0.601067i | \(-0.794742\pi\) |
0.920139 | + | 0.391593i | \(0.128076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1392 | − | 26.2218i | −0.690287 | − | 1.19561i | ||||
\(482\) | −0.176476 | + | 0.0931638i | −0.00803828 | + | 0.00424350i | ||||
\(483\) | −10.5184 | + | 2.66304i | −0.478602 | + | 0.121173i | ||||
\(484\) | −2.97011 | + | 4.34752i | −0.135005 | + | 0.197615i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.8342 | − | 17.1644i | −0.627531 | − | 0.778591i | ||||
\(487\) | −19.8270 | −0.898449 | −0.449225 | − | 0.893419i | \(-0.648300\pi\) | ||||
−0.449225 | + | 0.893419i | \(0.648300\pi\) | |||||||
\(488\) | 1.46132 | + | 1.08170i | 0.0661507 | + | 0.0489664i | ||||
\(489\) | 0.186200 | + | 0.735444i | 0.00842026 | + | 0.0332579i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2239 | + | 24.6365i | 0.641916 | + | 1.11183i | 0.985005 | + | 0.172528i | \(0.0551934\pi\) |
−0.343089 | + | 0.939303i | \(0.611473\pi\) | |||||||
\(492\) | 5.76586 | − | 15.7285i | 0.259945 | − | 0.709097i | ||||
\(493\) | 30.5090 | + | 17.6144i | 1.37406 | + | 0.793311i | ||||
\(494\) | −1.65117 | + | 43.5775i | −0.0742896 | + | 1.96065i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.14977 | + | 20.6327i | −0.141429 | + | 0.926438i | ||||
\(497\) | −1.27300 | + | 2.20490i | −0.0571018 | + | 0.0989031i | ||||
\(498\) | 3.45880 | − | 3.11844i | 0.154992 | − | 0.139741i | ||||
\(499\) | −4.89300 | + | 2.82497i | −0.219041 | + | 0.126463i | −0.605506 | − | 0.795841i | \(-0.707029\pi\) |
0.386465 | + | 0.922304i | \(0.373696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.03075 | + | 5.17185i | 0.224757 | + | 0.231061i | ||||
\(502\) | 11.3784 | + | 7.15700i | 0.507841 | + | 0.319433i | ||||
\(503\) | − | 32.7730i | − | 1.46128i | −0.682765 | − | 0.730638i | \(-0.739223\pi\) | ||
0.682765 | − | 0.730638i | \(-0.260777\pi\) | |||||||
\(504\) | 18.1819 | + | 2.58589i | 0.809886 | + | 0.115185i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.30422 | + | 10.0226i | −0.280257 | + | 0.445559i | ||||
\(507\) | 51.0652 | + | 14.4426i | 2.26788 | + | 0.641420i | ||||
\(508\) | 7.60794 | + | 15.8363i | 0.337548 | + | 0.702623i | ||||
\(509\) | 10.8656 | − | 6.27327i | 0.481610 | − | 0.278058i | −0.239477 | − | 0.970902i | \(-0.576976\pi\) |
0.721087 | + | 0.692844i | \(0.243643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.35861 | + | 2.51644i | 0.192813 | + | 0.111321i | ||||
\(512\) | −7.56409 | + | 21.3257i | −0.334289 | + | 0.942471i | ||||
\(513\) | −17.8476 | + | 16.4248i | −0.787990 | + | 0.725175i | ||||
\(514\) | −1.39139 | + | 36.7214i | −0.0613715 | + | 1.61971i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.61496 | − | 15.0330i | −0.115117 | − | 0.661790i | ||||
\(517\) | −0.0485608 | + | 0.0280366i | −0.00213570 | + | 0.00123305i | ||||
\(518\) | 6.54952 | + | 12.4065i | 0.287769 | + | 0.545109i | ||||
\(519\) | −14.9213 | − | 4.22016i | −0.654974 | − | 0.185245i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11.7475i | − | 0.514665i | −0.966323 | − | 0.257333i | \(-0.917156\pi\) | ||
0.966323 | − | 0.257333i | \(-0.0828436\pi\) | |||||||
\(522\) | 24.4222 | + | 16.3213i | 1.06893 | + | 0.714362i | ||||
\(523\) | −20.5196 | −0.897261 | −0.448630 | − | 0.893717i | \(-0.648088\pi\) | ||||
−0.448630 | + | 0.893717i | \(0.648088\pi\) | |||||||
\(524\) | 15.9380 | − | 23.3294i | 0.696255 | − | 1.01915i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.7446 | + | 33.6129i | 0.773703 | + | 1.46559i | ||||
\(527\) | 22.9933 | − | 13.2752i | 1.00160 | − | 0.578277i | ||||
\(528\) | 16.3099 | − | 11.6457i | 0.709796 | − | 0.506815i | ||||
\(529\) | −7.31125 | + | 12.6635i | −0.317881 | + | 0.550585i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.5803 | − | 12.6535i | −0.893109 | − | 0.549116i | ||||
\(532\) | 1.52901 | − | 20.1477i | 0.0662908 | − | 0.873515i | ||||
\(533\) | −15.9730 | + | 27.6660i | −0.691865 | + | 1.19835i | ||||
\(534\) | 8.68309 | + | 2.81499i | 0.375754 | + | 0.121817i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.5583 | − | 10.6733i | 1.06076 | − | 0.461016i | ||||
\(537\) | −4.47484 | − | 17.6745i | −0.193104 | − | 0.762711i | ||||
\(538\) | 12.3510 | − | 19.6359i | 0.532488 | − | 0.846562i | ||||
\(539\) | −6.69857 | −0.288528 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.0464 | 0.818871 | 0.409435 | − | 0.912339i | \(-0.365726\pi\) | ||||
0.409435 | + | 0.912339i | \(0.365726\pi\) | |||||||
\(542\) | −12.0840 | + | 19.2115i | −0.519054 | + | 0.825204i | ||||
\(543\) | −4.04216 | − | 15.9655i | −0.173466 | − | 0.685147i | ||||
\(544\) | 27.1908 | − | 9.44246i | 1.16580 | − | 0.404842i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −33.3145 | − | 10.8003i | −1.42573 | − | 0.462210i | ||||
\(547\) | 12.5453 | − | 21.7291i | 0.536399 | − | 0.929071i | −0.462695 | − | 0.886518i | \(-0.653117\pi\) |
0.999094 | − | 0.0425534i | \(-0.0135493\pi\) | |||||||
\(548\) | 30.3179 | + | 2.30082i | 1.29512 | + | 0.0982861i | ||||
\(549\) | 0.0533308 | − | 1.92766i | 0.00227610 | − | 0.0822706i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.1591 | − | 27.9884i | 0.688401 | − | 1.19235i | ||||
\(552\) | −11.2195 | + | 8.67077i | −0.477535 | + | 0.369052i | ||||
\(553\) | 31.8118 | − | 18.3665i | 1.35277 | − | 0.781024i | ||||
\(554\) | 16.0645 | + | 30.4303i | 0.682515 | + | 1.29286i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.19584 | − | 2.86649i | −0.177943 | − | 0.121566i | ||||
\(557\) | −4.13922 | −0.175384 | −0.0876922 | − | 0.996148i | \(-0.527949\pi\) | ||||
−0.0876922 | + | 0.996148i | \(0.527949\pi\) | |||||||
\(558\) | 19.8556 | − | 9.78971i | 0.840556 | − | 0.414431i | ||||
\(559\) | 29.0981i | 1.23072i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.5311 | − | 6.93807i | −1.03570 | − | 0.292926i | ||||
\(562\) | −6.89304 | − | 13.0572i | −0.290765 | − | 0.550784i | ||||
\(563\) | −25.8656 | + | 14.9335i | −1.09010 | + | 0.629372i | −0.933604 | − | 0.358306i | \(-0.883354\pi\) |
−0.156500 | + | 0.987678i | \(0.550021\pi\) | |||||||
\(564\) | −0.0661573 | + | 0.0115080i | −0.00278572 | + | 0.000484573i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.797262 | + | 21.0413i | −0.0335114 | + | 0.884431i | ||||
\(567\) | −8.79184 | − | 17.3819i | −0.369223 | − | 0.729970i | ||||
\(568\) | −0.377215 | + | 3.30577i | −0.0158276 | + | 0.138707i | ||||
\(569\) | 35.2116 | + | 20.3294i | 1.47615 | + | 0.852253i | 0.999638 | − | 0.0269176i | \(-0.00856919\pi\) |
0.476507 | + | 0.879170i | \(0.341903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.7953 | + | 20.0891i | −1.45614 | + | 0.840702i | −0.998818 | − | 0.0486002i | \(-0.984524\pi\) |
−0.457320 | + | 0.889302i | \(0.651191\pi\) | |||||||
\(572\) | −34.4484 | + | 16.5494i | −1.44036 | + | 0.691966i | ||||
\(573\) | −20.2681 | − | 5.73238i | −0.846712 | − | 0.239474i | ||||
\(574\) | 7.88094 | − | 12.5293i | 0.328944 | − | 0.522963i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 23.1388 | − | 6.37162i | 0.964115 | − | 0.265484i | ||||
\(577\) | − | 33.5865i | − | 1.39822i | −0.715013 | − | 0.699112i | \(-0.753579\pi\) | ||
0.715013 | − | 0.699112i | \(-0.246421\pi\) | |||||||
\(578\) | −10.6429 | − | 6.69441i | −0.442688 | − | 0.278451i | ||||
\(579\) | −16.9424 | − | 17.4176i | −0.704104 | − | 0.723853i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.56357 | − | 2.05743i | 0.147842 | − | 0.0853565i | ||||
\(582\) | −21.0335 | + | 18.9637i | −0.871866 | + | 0.786071i | ||||
\(583\) | −4.64615 | + | 8.04737i | −0.192424 | + | 0.333288i | ||||
\(584\) | 6.53479 | + | 0.745674i | 0.270412 | + | 0.0308562i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.39853 | + | 36.9098i | −0.0577726 | + | 1.52473i | ||||
\(587\) | −32.3717 | − | 18.6898i | −1.33612 | − | 0.771410i | −0.349892 | − | 0.936790i | \(-0.613782\pi\) |
−0.986230 | + | 0.165380i | \(0.947115\pi\) | |||||||
\(588\) | −7.53177 | − | 2.76104i | −0.310605 | − | 0.113863i | ||||
\(589\) | −12.1784 | − | 21.0937i | −0.501803 | − | 0.869149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.06739 | + | 12.1154i | 0.126176 | + | 0.498362i | ||||
\(592\) | 14.3124 | + | 11.4581i | 0.588236 | + | 0.470923i | ||||
\(593\) | −11.3789 | −0.467275 | −0.233638 | − | 0.972324i | \(-0.575063\pi\) | ||||
−0.233638 | + | 0.972324i | \(0.575063\pi\) | |||||||
\(594\) | −20.0314 | − | 7.11202i | −0.821900 | − | 0.291810i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.4123 | − | 7.79661i | −0.467468 | − | 0.319362i | ||||
\(597\) | 14.4920 | − | 3.66908i | 0.593116 | − | 0.150165i | ||||
\(598\) | 23.9126 | − | 12.6237i | 0.977859 | − | 0.516223i | ||||
\(599\) | −1.12135 | − | 1.94223i | −0.0458170 | − | 0.0793574i | 0.842207 | − | 0.539154i | \(-0.181256\pi\) |
−0.888024 | + | 0.459796i | \(0.847922\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.67140 | + | 15.0193i | −0.353714 | + | 0.612650i | −0.986897 | − | 0.161352i | \(-0.948415\pi\) |
0.633183 | + | 0.774002i | \(0.281748\pi\) | |||||||
\(602\) | 0.510483 | − | 13.4726i | 0.0208057 | − | 0.549103i | ||||
\(603\) | −24.1945 | − | 14.8757i | −0.985276 | − | 0.605784i | ||||
\(604\) | −3.22552 | + | 42.5027i | −0.131244 | + | 1.72941i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.8793 | + | 17.9231i | −0.807543 | + | 0.728078i | ||||
\(607\) | −8.50549 | − | 14.7319i | −0.345227 | − | 0.597951i | 0.640168 | − | 0.768235i | \(-0.278865\pi\) |
−0.985395 | + | 0.170284i | \(0.945531\pi\) | |||||||
\(608\) | −8.66234 | − | 24.9444i | −0.351304 | − | 1.01163i | ||||
\(609\) | 18.0968 | + | 18.6044i | 0.733321 | + | 0.753889i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.128055 | 0.00518056 | ||||||||
\(612\) | −24.7227 | − | 17.9124i | −0.999354 | − | 0.724065i | ||||
\(613\) | 6.23696i | 0.251908i | 0.992036 | + | 0.125954i | \(0.0401992\pi\) | ||||
−0.992036 | + | 0.125954i | \(0.959801\pi\) | |||||||
\(614\) | −34.1821 | − | 21.5005i | −1.37948 | − | 0.867691i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.2402 | − | 7.05815i | 0.654336 | − | 0.284381i | ||||
\(617\) | 4.18992 | + | 7.25716i | 0.168680 | + | 0.292162i | 0.937956 | − | 0.346754i | \(-0.112716\pi\) |
−0.769276 | + | 0.638917i | \(0.779383\pi\) | |||||||
\(618\) | −1.52201 | + | 0.324560i | −0.0612242 | + | 0.0130557i | ||||
\(619\) | 31.5019 | + | 18.1876i | 1.26617 | + | 0.731021i | 0.974260 | − | 0.225426i | \(-0.0723773\pi\) |
0.291906 | + | 0.956447i | \(0.405711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.3533 | + | 4.49175i | 0.575977 | + | 0.180248i | ||||
\(622\) | 0.00471451 | − | 0.124425i | 0.000189034 | − | 0.00498898i | ||||
\(623\) | 6.98476 | + | 4.03265i | 0.279839 | + | 0.161565i | ||||
\(624\) | −45.5547 | + | 4.40884i | −1.82365 | + | 0.176495i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.0461 | + | 19.0298i | 0.401521 | + | 0.760585i | ||||
\(627\) | −6.36487 | + | 22.5044i | −0.254188 | + | 0.898739i | ||||
\(628\) | −19.2715 | − | 13.1658i | −0.769015 | − | 0.525371i | ||||
\(629\) | − | 23.3220i | − | 0.929910i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.3747i | 1.68691i | 0.537199 | + | 0.843455i | \(0.319482\pi\) | ||||
−0.537199 | + | 0.843455i | \(0.680518\pi\) | |||||||
\(632\) | 28.5607 | − | 38.5838i | 1.13608 | − | 1.53478i | ||||
\(633\) | −22.4662 | − | 23.0963i | −0.892951 | − | 0.917997i | ||||
\(634\) | −8.96151 | + | 4.73088i | −0.355907 | + | 0.187887i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.54107 | + | 7.13328i | −0.338675 | + | 0.282853i | ||||
\(637\) | 13.2481 | + | 7.64881i | 0.524910 | + | 0.303057i | ||||
\(638\) | 28.3025 | + | 1.07239i | 1.12051 | + | 0.0424564i | ||||
\(639\) | 3.10388 | − | 1.67933i | 0.122787 | − | 0.0664332i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.58349 | − | 5.53303i | −0.378525 | − | 0.218542i | 0.298651 | − | 0.954362i | \(-0.403463\pi\) |
−0.677176 | + | 0.735821i | \(0.736797\pi\) | |||||||
\(642\) | −43.8176 | − | 14.2053i | −1.72934 | − | 0.560640i | ||||
\(643\) | 6.09436 | + | 10.5557i | 0.240338 | + | 0.416278i | 0.960811 | − | 0.277206i | \(-0.0894083\pi\) |
−0.720472 | + | 0.693484i | \(0.756075\pi\) | |||||||
\(644\) | −11.2932 | + | 5.42536i | −0.445013 | + | 0.213789i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.8843 | + | 28.4329i | −0.703649 | + | 1.11868i | ||||
\(647\) | 13.5692i | 0.533460i | 0.963771 | + | 0.266730i | \(0.0859432\pi\) | ||||
−0.963771 | + | 0.266730i | \(0.914057\pi\) | |||||||
\(648\) | −19.5916 | − | 16.2533i | −0.769631 | − | 0.638489i | ||||
\(649\) | −23.2945 | −0.914390 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.9623 | − | 4.80087i | 0.743189 | − | 0.188161i | ||||
\(652\) | 0.379342 | + | 0.789619i | 0.0148562 | + | 0.0309239i | ||||
\(653\) | 5.73470 | + | 9.93280i | 0.224416 | + | 0.388700i | 0.956144 | − | 0.292896i | \(-0.0946191\pi\) |
−0.731728 | + | 0.681597i | \(0.761286\pi\) | |||||||
\(654\) | 2.56121 | − | 7.90028i | 0.100151 | − | 0.308925i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.91915 | − | 19.1221i | 0.113974 | − | 0.746592i | ||||
\(657\) | −3.31967 | − | 6.13569i | −0.129513 | − | 0.239376i | ||||
\(658\) | −0.0592905 | − | 0.00224654i | −0.00231138 | − | 8.75792e-5i | ||||
\(659\) | 8.46548 | − | 14.6626i | 0.329768 | − | 0.571175i | −0.652698 | − | 0.757619i | \(-0.726363\pi\) |
0.982466 | + | 0.186443i | \(0.0596961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.92555 | + | 11.9954i | 0.269373 | + | 0.466567i | 0.968700 | − | 0.248234i | \(-0.0798503\pi\) |
−0.699327 | + | 0.714802i | \(0.746517\pi\) | |||||||
\(662\) | 0.541154 | + | 1.02509i | 0.0210326 | + | 0.0398411i | ||||
\(663\) | 40.5942 | + | 41.7329i | 1.57655 | + | 1.62077i | ||||
\(664\) | 3.19938 | − | 4.32218i | 0.124160 | − | 0.167733i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.27341 | − | 19.4043i | 0.0493437 | − | 0.751901i | ||||
\(667\) | −20.0393 | −0.775925 | ||||||||
\(668\) | 6.87911 | + | 4.69962i | 0.266161 | + | 0.181834i | ||||
\(669\) | −20.5730 | − | 5.81860i | −0.795397 | − | 0.224960i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.929695 | − | 1.61028i | −0.0358905 | − | 0.0621642i | ||||
\(672\) | 21.1695 | − | 1.24213i | 0.816631 | − | 0.0479164i | ||||
\(673\) | 13.3158 | + | 7.68786i | 0.513285 | + | 0.296345i | 0.734183 | − | 0.678952i | \(-0.237565\pi\) |
−0.220898 | + | 0.975297i | \(0.570899\pi\) | |||||||
\(674\) | −4.33542 | − | 0.164271i | −0.166994 | − | 0.00632748i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 61.1022 | + | 4.63703i | 2.35009 | + | 0.178347i | ||||
\(677\) | −19.8641 | + | 34.4057i | −0.763441 | + | 1.32232i | 0.177626 | + | 0.984098i | \(0.443158\pi\) |
−0.941067 | + | 0.338221i | \(0.890175\pi\) | |||||||
\(678\) | −2.39133 | + | 0.509937i | −0.0918384 | + | 0.0195840i | ||||
\(679\) | −21.6706 | + | 12.5115i | −0.831642 | + | 0.480149i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.350731 | + | 1.24009i | −0.0134400 | + | 0.0475202i | ||||
\(682\) | 11.3651 | − | 18.0685i | 0.435193 | − | 0.691879i | ||||
\(683\) | 21.6572i | 0.828690i | 0.910120 | + | 0.414345i | \(0.135989\pi\) | ||||
−0.910120 | + | 0.414345i | \(0.864011\pi\) | |||||||
\(684\) | −16.4325 | + | 22.6801i | −0.628313 | + | 0.867196i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.1360 | − | 15.1816i | −0.921518 | − | 0.579635i | ||||
\(687\) | 32.4751 | − | 31.5891i | 1.23900 | − | 1.20520i | ||||
\(688\) | −6.40603 | − | 16.4134i | −0.244228 | − | 0.625756i | ||||
\(689\) | 18.3779 | − | 10.6105i | 0.700143 | − | 0.404228i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3770 | + | 8.87791i | 0.584968 | + | 0.337732i | 0.763105 | − | 0.646274i | \(-0.223674\pi\) |
−0.178137 | + | 0.984006i | \(0.557007\pi\) | |||||||
\(692\) | −17.8542 | − | 1.35495i | −0.678714 | − | 0.0515075i | ||||
\(693\) | −15.9996 | − | 9.83715i | −0.607774 | − | 0.373682i | ||||
\(694\) | 31.5324 | + | 1.19477i | 1.19695 | + | 0.0453530i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 31.3809 | + | 12.8716i | 1.18949 | + | 0.487897i | ||||
\(697\) | −21.3098 | + | 12.3032i | −0.807167 | + | 0.466018i | ||||
\(698\) | 12.5556 | − | 6.62822i | 0.475235 | − | 0.250882i | ||||
\(699\) | 10.9790 | + | 43.3644i | 0.415265 | + | 1.64019i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.3642i | 1.44900i | 0.689277 | + | 0.724498i | \(0.257928\pi\) | ||||
−0.689277 | + | 0.724498i | \(0.742072\pi\) | |||||||
\(702\) | 31.4964 | + | 36.9389i | 1.18875 | + | 1.39417i | ||||
\(703\) | −21.3952 | −0.806936 | ||||||||
\(704\) | 15.7880 | − | 16.9190i | 0.595033 | − | 0.637658i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.9235 | + | 8.40622i | −0.599290 | + | 0.316372i | ||||
\(707\) | −20.4815 | + | 11.8250i | −0.770287 | + | 0.444725i | ||||
\(708\) | −26.1920 | − | 9.60162i | −0.984357 | − | 0.360851i | ||||
\(709\) | 1.96851 | − | 3.40955i | 0.0739288 | − | 0.128049i | −0.826691 | − | 0.562656i | \(-0.809780\pi\) |
0.900620 | + | 0.434608i | \(0.143113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −50.8969 | − | 1.40812i | −1.90878 | − | 0.0528085i | ||||
\(712\) | 10.4721 | + | 1.19496i | 0.392460 | + | 0.0447829i | ||||
\(713\) | −7.55138 | + | 13.0794i | −0.282802 | + | 0.489827i | ||||
\(714\) | −18.0633 | − | 20.0348i | −0.676001 | − | 0.749782i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.11650 | − | 18.9764i | −0.340699 | − | 0.709183i | ||||
\(717\) | 10.2206 | − | 9.94172i | 0.381694 | − | 0.371280i | ||||
\(718\) | −7.10240 | − | 4.46742i | −0.265059 | − | 0.166722i | ||||
\(719\) | 25.9983 | 0.969573 | 0.484787 | − | 0.874632i | \(-0.338897\pi\) | ||||
0.484787 | + | 0.874632i | \(0.338897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.37505 | −0.0512097 | ||||||||
\(722\) | 3.33908 | + | 2.10028i | 0.124268 | + | 0.0781644i | ||||
\(723\) | 0.235182 | + | 0.0665161i | 0.00874652 | + | 0.00247376i | ||||
\(724\) | −8.23501 | − | 17.1416i | −0.306052 | − | 0.637062i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.30675 | − | 1.34488i | 0.234065 | − | 0.0499132i | ||||
\(727\) | −13.4108 | + | 23.2282i | −0.497379 | + | 0.861486i | −0.999995 | − | 0.00302389i | \(-0.999037\pi\) |
0.502616 | + | 0.864510i | \(0.332371\pi\) | |||||||
\(728\) | −40.1786 | − | 4.58470i | −1.48912 | − | 0.169920i | ||||
\(729\) | −2.23781 | + | 26.9071i | −0.0828818 | + | 0.996559i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.2065 | + | 19.4102i | −0.414486 | + | 0.717911i | ||||
\(732\) | −0.381605 | − | 2.19378i | −0.0141045 | − | 0.0810845i | ||||
\(733\) | 13.8581 | − | 8.00096i | 0.511859 | − | 0.295522i | −0.221738 | − | 0.975106i | \(-0.571173\pi\) |
0.733598 | + | 0.679584i | \(0.237840\pi\) | |||||||
\(734\) | 33.2681 | − | 17.5626i | 1.22795 | − | 0.648248i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.7093 | + | 12.3851i | −0.394749 | + | 0.456522i | ||||
\(737\) | −27.3854 | −1.00875 | ||||||||
\(738\) | −18.4019 | + | 9.07295i | −0.677383 | + | 0.333980i | ||||
\(739\) | − | 2.17451i | − | 0.0799905i | −0.999200 | − | 0.0399952i | \(-0.987266\pi\) | ||
0.999200 | − | 0.0399952i | \(-0.0127343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.2850 | − | 37.2404i | 1.40643 | − | 1.36806i | ||||
\(742\) | −8.69525 | + | 4.59032i | −0.319213 | + | 0.168516i | ||||
\(743\) | 15.8760 | − | 9.16604i | 0.582436 | − | 0.336269i | −0.179665 | − | 0.983728i | \(-0.557501\pi\) |
0.762101 | + | 0.647458i | \(0.224168\pi\) | |||||||
\(744\) | 20.2263 | − | 15.6315i | 0.741533 | − | 0.573077i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 37.3917 | + | 1.41679i | 1.36901 | + | 0.0518722i | ||||
\(747\) | −5.70150 | − | 0.157738i | −0.208607 | − | 0.00577133i | ||||
\(748\) | −29.3528 | − | 2.22758i | −1.07324 | − | 0.0814483i | ||||
\(749\) | −35.2473 | − | 20.3500i | −1.28791 | − | 0.743574i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.9363 | + | 13.8196i | −0.873449 | + | 0.504286i | −0.868493 | − | 0.495702i | \(-0.834911\pi\) |
−0.00495598 | + | 0.999988i | \(0.501578\pi\) | |||||||
\(752\) | −0.0722324 | + | 0.0281917i | −0.00263404 | + | 0.00102805i | ||||
\(753\) | −4.04065 | − | 15.9596i | −0.147250 | − | 0.581599i | ||||
\(754\) | −54.7509 | − | 34.4383i | −1.99391 | − | 1.25417i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.9350 | − | 17.6555i | −0.506811 | − | 0.642125i | ||||
\(757\) | 47.4098i | 1.72314i | 0.507640 | + | 0.861570i | \(0.330518\pi\) | ||||
−0.507640 | + | 0.861570i | \(0.669482\pi\) | |||||||
\(758\) | −16.0652 | + | 25.5409i | −0.583515 | + | 0.927686i | ||||
\(759\) | 14.0579 | − | 3.55920i | 0.510271 | − | 0.129191i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.6920 | + | 11.3692i | −0.713834 | + | 0.412132i | −0.812479 | − | 0.582990i | \(-0.801883\pi\) |
0.0986449 | + | 0.995123i | \(0.468549\pi\) | |||||||
\(762\) | 6.63582 | − | 20.4688i | 0.240390 | − | 0.741505i | ||||
\(763\) | 3.66910 | − | 6.35506i | 0.132830 | − | 0.230069i | ||||
\(764\) | −24.2519 | − | 1.84047i | −0.877402 | − | 0.0665858i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.45656 | + | 0.168861i | 0.161022 | + | 0.00610119i | ||||
\(767\) | 46.0709 | + | 26.5990i | 1.66352 | + | 0.960436i | ||||
\(768\) | 24.7255 | − | 12.5159i | 0.892206 | − | 0.451629i | ||||
\(769\) | 17.4807 | + | 30.2775i | 0.630371 | + | 1.09183i | 0.987476 | + | 0.157770i | \(0.0504305\pi\) |
−0.357105 | + | 0.934064i | \(0.616236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.2615 | − | 31.3813i | 1.16187 | − | 1.13017i | ||||
\(772\) | −23.1673 | − | 15.8273i | −0.833810 | − | 0.569637i | ||||
\(773\) | −5.74824 | −0.206750 | −0.103375 | − | 0.994642i | \(-0.532964\pi\) | ||||
−0.103375 | + | 0.994642i | \(0.532964\pi\) | |||||||
\(774\) | −10.3838 | + | 15.5377i | −0.373237 | + | 0.558490i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.4559 | + | 26.2838i | −0.698427 | + | 0.943534i | ||||
\(777\) | 4.67615 | − | 16.5336i | 0.167756 | − | 0.593138i | ||||
\(778\) | 9.90674 | + | 18.7659i | 0.355174 | + | 0.672791i | ||||
\(779\) | 11.2868 | + | 19.5493i | 0.404391 | + | 0.700425i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.70138 | − | 2.94688i | 0.0608802 | − | 0.105448i | ||||
\(782\) | 20.8129 | + | 0.788608i | 0.744267 | + | 0.0282006i | ||||
\(783\) | −7.86185 | − | 35.1060i | −0.280959 | − | 1.25459i | ||||
\(784\) | −9.15681 | − | 1.39787i | −0.327029 | − | 0.0499238i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.8428 | + | 7.21680i | −1.20713 | + | 0.257415i | ||||
\(787\) | −26.5020 | − | 45.9027i | −0.944693 | − | 1.63626i | −0.756366 | − | 0.654149i | \(-0.773027\pi\) |
−0.188327 | − | 0.982106i | \(-0.560306\pi\) | |||||||
\(788\) | 6.24913 | + | 13.0079i | 0.222616 | + | 0.463386i | ||||
\(789\) | 12.6691 | − | 44.7944i | 0.451032 | − | 1.59472i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.16043 | −0.0768162 | ||||||||
\(792\) | −24.3004 | − | 3.45608i | −0.863476 | − | 0.122806i | ||||
\(793\) | 4.24632i | 0.150791i | ||||||||
\(794\) | 7.56543 | − | 12.0277i | 0.268487 | − | 0.426847i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.5595 | − | 7.47494i | 0.551491 | − | 0.264942i | ||||
\(797\) | −6.93917 | − | 12.0190i | −0.245798 | − | 0.425735i | 0.716558 | − | 0.697528i | \(-0.245717\pi\) |
−0.962356 | + | 0.271793i | \(0.912383\pi\) | |||||||
\(798\) | −18.3795 | + | 16.5709i | −0.650629 | + | 0.586604i | ||||
\(799\) | 0.0854205 | + | 0.0493176i | 0.00302196 | + | 0.00174473i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.31984 | − | 9.83258i | −0.187967 | − | 0.347417i | ||||
\(802\) | 11.1805 | + | 0.423633i | 0.394796 | + | 0.0149590i | ||||
\(803\) | −5.82534 | − | 3.36326i | −0.205572 | − | 0.118687i | ||||
\(804\) | −30.7917 | − | 11.2878i | −1.08594 | − | 0.398090i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −43.1091 | + | 22.7578i | −1.51845 | + | 0.801609i | ||||
\(807\) | −27.5417 | + | 6.97303i | −0.969515 | + | 0.245462i | ||||
\(808\) | −18.3884 | + | 24.8416i | −0.646900 | + | 0.873924i | ||||
\(809\) | − | 46.1210i | − | 1.62153i | −0.585372 | − | 0.810765i | \(-0.699052\pi\) | ||
0.585372 | − | 0.810765i | \(-0.300948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.7719i | − | 1.11566i | −0.829954 | − | 0.557832i | \(-0.811633\pi\) | ||
0.829954 | − | 0.557832i | \(-0.188367\pi\) | |||||||
\(812\) | 24.7459 | + | 16.9057i | 0.868409 | + | 0.593274i | ||||
\(813\) | 26.9465 | − | 6.82233i | 0.945055 | − | 0.239269i | ||||
\(814\) | −8.75353 | − | 16.5814i | −0.306811 | − | 0.581179i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −32.0857 | − | 14.6034i | −1.12322 | − | 0.511221i | ||||
\(817\) | 17.8065 | + | 10.2806i | 0.622972 | + | 0.359673i | ||||
\(818\) | 1.45459 | − | 38.3894i | 0.0508585 | − | 1.34225i | ||||
\(819\) | 20.4107 | + | 37.7247i | 0.713207 | + | 1.31821i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.7695 | + | 6.79511i | 0.410758 | + | 0.237151i | 0.691115 | − | 0.722745i | \(-0.257120\pi\) |
−0.280358 | + | 0.959896i | \(0.590453\pi\) | |||||||
\(822\) | −24.9356 | − | 27.6572i | −0.869729 | − | 0.964655i | ||||
\(823\) | 14.8238 | + | 25.6756i | 0.516725 | + | 0.894995i | 0.999811 | + | 0.0194217i | \(0.00618250\pi\) |
−0.483086 | + | 0.875573i | \(0.660484\pi\) | |||||||
\(824\) | −1.64806 | + | 0.716264i | −0.0574129 | + | 0.0249522i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.8645 | − | 13.1238i | −0.725969 | − | 0.456635i | ||||
\(827\) | 24.1020i | 0.838110i | 0.907961 | + | 0.419055i | \(0.137639\pi\) | ||||
−0.907961 | + | 0.419055i | \(0.862361\pi\) | |||||||
\(828\) | 17.2736 | + | 1.79254i | 0.600299 | + | 0.0622952i | ||||
\(829\) | −42.6555 | −1.48149 | −0.740743 | − | 0.671789i | \(-0.765526\pi\) | ||||
−0.740743 | + | 0.671789i | \(0.765526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.4696 | − | 40.5532i | 0.397874 | − | 1.40677i | ||||
\(832\) | −50.5439 | + | 15.4340i | −1.75229 | + | 0.535077i | ||||
\(833\) | 5.89153 | + | 10.2044i | 0.204130 | + | 0.353563i | ||||
\(834\) | 1.29796 | + | 6.08671i | 0.0449446 | + | 0.210766i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.04354 | + | 26.9277i | −0.0706773 | + | 0.931315i | ||||
\(837\) | −25.8758 | − | 8.09763i | −0.894398 | − | 0.279895i | ||||
\(838\) | −0.458924 | + | 12.1119i | −0.0158533 | + | 0.418398i | ||||
\(839\) | −9.56807 | + | 16.5724i | −0.330327 | + | 0.572142i | −0.982576 | − | 0.185862i | \(-0.940492\pi\) |
0.652249 | + | 0.758005i | \(0.273826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.46742 | + | 16.3981i | 0.326463 | + | 0.565450i | ||||
\(842\) | −8.54196 | + | 4.50940i | −0.294376 | + | 0.155404i | ||||
\(843\) | −4.92141 | + | 17.4007i | −0.169502 | + | 0.599314i | ||||
\(844\) | −30.7206 | − | 20.9875i | −1.05745 | − | 0.722419i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.0683784 | + | 0.0456971i | 0.00235090 | + | 0.00157110i | ||||
\(847\) | 5.69781 | 0.195779 | ||||||||
\(848\) | −8.03054 | + | 10.0310i | −0.275770 | + | 0.344467i | ||||
\(849\) | 18.4858 | − | 17.9814i | 0.634430 | − | 0.617121i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.63318 | + | 11.4890i | 0.227383 | + | 0.393838i | ||||
\(852\) | 3.12766 | − | 2.61215i | 0.107152 | − | 0.0894906i | ||||
\(853\) | −25.0942 | − | 14.4881i | −0.859207 | − | 0.496064i | 0.00453935 | − | 0.999990i | \(-0.498555\pi\) |
−0.863747 | + | 0.503926i | \(0.831888\pi\) | |||||||
\(854\) | 0.0744954 | − | 1.96608i | 0.00254918 | − | 0.0672777i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −52.8457 | − | 6.03013i | −1.80623 | − | 0.206106i | ||||
\(857\) | −8.12743 | + | 14.0771i | −0.277628 | + | 0.480865i | −0.970795 | − | 0.239912i | \(-0.922882\pi\) |
0.693167 | + | 0.720777i | \(0.256215\pi\) | |||||||
\(858\) | 44.5253 | + | 14.4348i | 1.52007 | + | 0.492795i | ||||
\(859\) | 39.4268 | − | 22.7631i | 1.34523 | − | 0.776666i | 0.357657 | − | 0.933853i | \(-0.383576\pi\) |
0.987569 | + | 0.157187i | \(0.0502425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.5739 | + | 4.44937i | −0.598917 | + | 0.151634i | ||||
\(862\) | −31.7890 | − | 19.9953i | −1.08274 | − | 0.681043i | ||||
\(863\) | 14.4497i | 0.491875i | 0.969286 | + | 0.245937i | \(0.0790957\pi\) | ||||
−0.969286 | + | 0.245937i | \(0.920904\pi\) | |||||||
\(864\) | −25.8984 | − | 13.9022i | −0.881083 | − | 0.472962i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.39064 | + | 14.9295i | −0.319107 | + | 0.507324i | ||||
\(867\) | 3.77949 | + | 14.9280i | 0.128358 | + | 0.506983i | ||||
\(868\) | 20.3591 | − | 9.78072i | 0.691032 | − | 0.331979i | ||||
\(869\) | −42.5169 | + | 24.5471i | −1.44229 | + | 0.832705i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.1616 | + | 31.2702i | 1.83520 | + | 1.05955i | ||||
\(872\) | 1.08723 | − | 9.52804i | 0.0368182 | − | 0.322660i | ||||
\(873\) | 34.6717 | + | 0.959228i | 1.17346 | + | 0.0324650i | ||||
\(874\) | 0.723455 | − | 19.0934i | 0.0244712 | − | 0.645843i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.16365 | − | 6.18272i | −0.174464 | − | 0.208895i | ||||
\(877\) | 20.7046 | − | 11.9538i | 0.699144 | − | 0.403651i | −0.107885 | − | 0.994163i | \(-0.534408\pi\) |
0.807029 | + | 0.590512i | \(0.201074\pi\) | |||||||
\(878\) | 9.78970 | + | 18.5442i | 0.330386 | + | 0.625837i | ||||
\(879\) | 32.4270 | − | 31.5423i | 1.09374 | − | 1.06390i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 51.7852i | − | 1.74469i | −0.488893 | − | 0.872344i | \(-0.662599\pi\) | ||
0.488893 | − | 0.872344i | \(-0.337401\pi\) | |||||||
\(882\) | 4.34467 | + | 8.81194i | 0.146293 | + | 0.296713i | ||||
\(883\) | −17.1884 | −0.578436 | −0.289218 | − | 0.957263i | \(-0.593395\pi\) | ||||
−0.289218 | + | 0.957263i | \(0.593395\pi\) | |||||||
\(884\) | 55.5091 | + | 37.9223i | 1.86697 | + | 1.27547i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.0955 | − | 49.4316i | −0.876695 | − | 1.66069i | ||||
\(887\) | 15.4564 | − | 8.92377i | 0.518976 | − | 0.299631i | −0.217540 | − | 0.976051i | \(-0.569803\pi\) |
0.736515 | + | 0.676421i | \(0.236470\pi\) | |||||||
\(888\) | −3.00774 | − | 22.2520i | −0.100933 | − | 0.746728i | ||||
\(889\) | 9.50623 | − | 16.4653i | 0.318829 | − | 0.552227i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.7504 | + | 23.2311i | 0.393654 | + | 0.778273i | ||||
\(892\) | −24.6167 | − | 1.86815i | −0.824227 | − | 0.0625504i | ||||
\(893\) | 0.0452431 | − | 0.0783633i | 0.00151400 | − | 0.00262233i | ||||
\(894\) | 3.53034 | + | 16.5554i | 0.118072 | + | 0.553694i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.6729 | − | 6.25932i | 0.790857 | − | 0.209109i | ||||
\(897\) | −31.8673 | − | 9.01295i | −1.06402 | − | 0.300934i | ||||
\(898\) | 17.1975 | − | 27.3411i | 0.573890 | − | 0.912383i | ||||
\(899\) | 36.1264 | 1.20488 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.3456 | 0.544550 | ||||||||
\(902\) | −10.5330 | + | 16.7456i | −0.350711 | + | 0.557568i | ||||
\(903\) | −11.8364 | + | 11.5134i | −0.393889 | + | 0.383142i | ||||
\(904\) | −2.58937 | + | 1.12537i | −0.0861213 | + | 0.0374292i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 38.7726 | − | 34.9572i | 1.28813 | − | 1.16138i | ||||
\(907\) | 1.17993 | − | 2.04370i | 0.0391790 | − | 0.0678600i | −0.845771 | − | 0.533546i | \(-0.820859\pi\) |
0.884950 | + | 0.465686i | \(0.154192\pi\) | |||||||
\(908\) | −0.112608 | + | 1.48383i | −0.00373701 | + | 0.0492427i | ||||
\(909\) | 32.7692 | + | 0.906594i | 1.08688 | + | 0.0300698i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.6895 | − | 32.3712i | 0.619212 | − | 1.07251i | −0.370418 | − | 0.928865i | \(-0.620786\pi\) |
0.989630 | − | 0.143641i | \(-0.0458810\pi\) | |||||||
\(912\) | −13.3969 | + | 29.4349i | −0.443616 | + | 0.974685i | ||||
\(913\) | −4.76277 | + | 2.74978i | −0.157625 | + | 0.0910046i | ||||
\(914\) | −0.549626 | − | 1.04113i | −0.0181800 | − | 0.0344377i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.5099 | − | 43.1953i | 0.975034 | − | 1.42721i | ||||
\(917\) | −30.5752 | −1.00968 | ||||||||
\(918\) | 6.78380 | + | 36.7706i | 0.223899 | + | 1.21361i | ||||
\(919\) | − | 4.73062i | − | 0.156049i | −0.996951 | − | 0.0780243i | \(-0.975139\pi\) | ||
0.996951 | − | 0.0780243i | \(-0.0248612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.1386 | + | 47.9446i | 0.399982 | + | 1.57983i | ||||
\(922\) | 23.6246 | + | 44.7512i | 0.778036 | + | 1.47380i | ||||
\(923\) | −6.72983 | + | 3.88547i | −0.221515 | + | 0.127892i | ||||
\(924\) | −20.3623 | − | 7.46452i | −0.669870 | − | 0.245565i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.445908 | − | 11.7684i | 0.0146534 | − | 0.386732i | ||||
\(927\) | 1.62365 | + | 0.998278i | 0.0533275 | + | 0.0327877i | ||||
\(928\) | 38.4651 | + | 7.37214i | 1.26268 | + | 0.242002i | ||||
\(929\) | −25.4661 | − | 14.7029i | −0.835517 | − | 0.482386i | 0.0202209 | − | 0.999796i | \(-0.493563\pi\) |
−0.855738 | + | 0.517410i | \(0.826896\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.36137 | − | 5.40479i | 0.306806 | − | 0.177135i | ||||
\(932\) | 22.3674 | + | 46.5588i | 0.732667 | + | 1.52508i | ||||
\(933\) | −0.109313 | + | 0.106331i | −0.00357876 | + | 0.00348112i | ||||
\(934\) | 12.6956 | − | 20.1838i | 0.415414 | − | 0.660435i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 44.1139 | + | 34.5829i | 1.44191 | + | 1.13038i | ||||
\(937\) | − | 20.2810i | − | 0.662551i | −0.943534 | − | 0.331276i | \(-0.892521\pi\) | ||
0.943534 | − | 0.331276i | \(-0.107479\pi\) | |||||||
\(938\) | −24.5286 | − | 15.4285i | −0.800888 | − | 0.503759i | ||||
\(939\) | 7.17257 | − | 25.3602i | 0.234068 | − | 0.827600i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.09878 | + | 4.09848i | −0.231413 | + | 0.133607i | −0.611224 | − | 0.791458i | \(-0.709323\pi\) |
0.379810 | + | 0.925064i | \(0.375989\pi\) | |||||||
\(942\) | 5.96151 | + | 27.9562i | 0.194236 | + | 0.910863i | ||||
\(943\) | 6.99850 | − | 12.1218i | 0.227903 | − | 0.394739i | ||||
\(944\) | −31.8432 | − | 4.86114i | −1.03641 | − | 0.158217i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.682268 | + | 18.0064i | −0.0221824 | + | 0.585437i | ||||
\(947\) | −36.4493 | − | 21.0440i | −1.18444 | − | 0.683839i | −0.227405 | − | 0.973800i | \(-0.573024\pi\) |
−0.957038 | + | 0.289962i | \(0.906357\pi\) | |||||||
\(948\) | −57.9233 | + | 10.0757i | −1.88126 | + | 0.327243i | ||||
\(949\) | 7.68074 | + | 13.3034i | 0.249327 | + | 0.431848i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.9426 | + | 3.37770i | 0.387266 | + | 0.109530i | ||||
\(952\) | −25.0358 | − | 18.5321i | −0.811415 | − | 0.600630i | ||||
\(953\) | −17.5687 | −0.569106 | −0.284553 | − | 0.958660i | \(-0.591845\pi\) | ||||
−0.284553 | + | 0.958660i | \(0.591845\pi\) | |||||||
\(954\) | 13.5998 | + | 0.892488i | 0.440309 | + | 0.0288954i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.28735 | − | 13.5944i | 0.300375 | − | 0.439675i | ||||
\(957\) | −24.1867 | − | 24.8651i | −0.781845 | − | 0.803774i | ||||
\(958\) | −6.62065 | + | 3.49512i | −0.213904 | + | 0.112922i | ||||
\(959\) | −16.4516 | − | 28.4950i | −0.531249 | − | 0.920150i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.88653 | + | 3.26756i | −0.0608557 | + | 0.105405i | ||||
\(962\) | −1.62130 | + | 42.7893i | −0.0522730 | + | 1.37958i | ||||
\(963\) | 26.8456 | + | 49.6183i | 0.865087 | + | 1.59893i | ||||
\(964\) | 0.281408 | + | 0.0213560i | 0.00906356 | + | 0.000687831i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.5966 | + | 4.73212i | 0.469639 | + | 0.152253i | ||||
\(967\) | 11.6316 | + | 20.1466i | 0.374048 | + | 0.647870i | 0.990184 | − | 0.139770i | \(-0.0446362\pi\) |
−0.616136 | + | 0.787640i | \(0.711303\pi\) | |||||||
\(968\) | 6.82907 | − | 2.96798i | 0.219495 | − | 0.0953944i | ||||
\(969\) | 39.8807 | − | 10.0970i | 1.28115 | − | 0.324363i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2618 | −0.810688 | −0.405344 | − | 0.914164i | \(-0.632848\pi\) | ||||
−0.405344 | + | 0.914164i | \(0.632848\pi\) | |||||||
\(972\) | 3.63651 | + | 30.9641i | 0.116641 | + | 0.993174i | ||||
\(973\) | 5.49901i | 0.176290i | ||||||||
\(974\) | 23.7348 | + | 14.9292i | 0.760513 | + | 0.478363i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.934840 | − | 2.39523i | −0.0299235 | − | 0.0766695i | ||||
\(977\) | −12.4595 | − | 21.5806i | −0.398616 | − | 0.690423i | 0.594939 | − | 0.803771i | \(-0.297176\pi\) |
−0.993555 | + | 0.113347i | \(0.963843\pi\) | |||||||
\(978\) | 0.330870 | − | 1.02060i | 0.0105801 | − | 0.0326351i | ||||
\(979\) | −9.33524 | − | 5.38970i | −0.298355 | − | 0.172256i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.94614 | + | 4.84024i | −0.285628 | + | 0.154537i | ||||
\(982\) | 1.52329 | − | 40.2024i | 0.0486100 | − | 1.28291i | ||||
\(983\) | −13.8502 | − | 7.99642i | −0.441753 | − | 0.255046i | 0.262588 | − | 0.964908i | \(-0.415424\pi\) |
−0.704341 | + | 0.709862i | \(0.748757\pi\) | |||||||
\(984\) | −18.7454 | + | 14.4870i | −0.597582 | + | 0.461828i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −23.2590 | − | 44.0585i | −0.740716 | − | 1.40311i | ||||
\(987\) | 0.0506684 | + | 0.0520896i | 0.00161279 | + | 0.00165803i | ||||
\(988\) | 34.7893 | − | 50.9231i | 1.10679 | − | 1.62008i | ||||
\(989\) | − | 12.7492i | − | 0.405402i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 29.4708i | − | 0.936171i | −0.883683 | − | 0.468085i | \(-0.844944\pi\) | ||
0.883683 | − | 0.468085i | \(-0.155056\pi\) | |||||||
\(992\) | 19.3065 | − | 22.3276i | 0.612981 | − | 0.708903i | ||||
\(993\) | 0.386367 | − | 1.36609i | 0.0122610 | − | 0.0433514i | ||||
\(994\) | 3.18412 | − | 1.68093i | 0.100994 | − | 0.0533160i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.48860 | + | 1.12868i | −0.205599 | + | 0.0357637i | ||||
\(997\) | 33.5185 | + | 19.3519i | 1.06154 | + | 0.612881i | 0.925858 | − | 0.377871i | \(-0.123344\pi\) |
0.135683 | + | 0.990752i | \(0.456677\pi\) | |||||||
\(998\) | 7.98451 | + | 0.302536i | 0.252745 | + | 0.00957661i | ||||
\(999\) | −17.5248 | + | 16.1278i | −0.554459 | + | 0.510260i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.2.o.b.299.5 | 48 | ||
4.3 | odd | 2 | inner | 900.2.o.b.299.21 | 48 | ||
5.2 | odd | 4 | 180.2.q.a.11.17 | yes | 48 | ||
5.3 | odd | 4 | 900.2.r.f.551.8 | 48 | |||
5.4 | even | 2 | 900.2.o.c.299.20 | 48 | |||
9.5 | odd | 6 | 900.2.o.c.599.4 | 48 | |||
15.2 | even | 4 | 540.2.q.a.251.8 | 48 | |||
20.3 | even | 4 | 900.2.r.f.551.16 | 48 | |||
20.7 | even | 4 | 180.2.q.a.11.9 | ✓ | 48 | ||
20.19 | odd | 2 | 900.2.o.c.299.4 | 48 | |||
36.23 | even | 6 | 900.2.o.c.599.20 | 48 | |||
45.2 | even | 12 | 1620.2.e.b.971.48 | 48 | |||
45.7 | odd | 12 | 1620.2.e.b.971.1 | 48 | |||
45.14 | odd | 6 | inner | 900.2.o.b.599.21 | 48 | ||
45.22 | odd | 12 | 540.2.q.a.71.16 | 48 | |||
45.23 | even | 12 | 900.2.r.f.851.16 | 48 | |||
45.32 | even | 12 | 180.2.q.a.131.9 | yes | 48 | ||
60.47 | odd | 4 | 540.2.q.a.251.16 | 48 | |||
180.7 | even | 12 | 1620.2.e.b.971.47 | 48 | |||
180.23 | odd | 12 | 900.2.r.f.851.8 | 48 | |||
180.47 | odd | 12 | 1620.2.e.b.971.2 | 48 | |||
180.59 | even | 6 | inner | 900.2.o.b.599.5 | 48 | ||
180.67 | even | 12 | 540.2.q.a.71.8 | 48 | |||
180.167 | odd | 12 | 180.2.q.a.131.17 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.2.q.a.11.9 | ✓ | 48 | 20.7 | even | 4 | ||
180.2.q.a.11.17 | yes | 48 | 5.2 | odd | 4 | ||
180.2.q.a.131.9 | yes | 48 | 45.32 | even | 12 | ||
180.2.q.a.131.17 | yes | 48 | 180.167 | odd | 12 | ||
540.2.q.a.71.8 | 48 | 180.67 | even | 12 | |||
540.2.q.a.71.16 | 48 | 45.22 | odd | 12 | |||
540.2.q.a.251.8 | 48 | 15.2 | even | 4 | |||
540.2.q.a.251.16 | 48 | 60.47 | odd | 4 | |||
900.2.o.b.299.5 | 48 | 1.1 | even | 1 | trivial | ||
900.2.o.b.299.21 | 48 | 4.3 | odd | 2 | inner | ||
900.2.o.b.599.5 | 48 | 180.59 | even | 6 | inner | ||
900.2.o.b.599.21 | 48 | 45.14 | odd | 6 | inner | ||
900.2.o.c.299.4 | 48 | 20.19 | odd | 2 | |||
900.2.o.c.299.20 | 48 | 5.4 | even | 2 | |||
900.2.o.c.599.4 | 48 | 9.5 | odd | 6 | |||
900.2.o.c.599.20 | 48 | 36.23 | even | 6 | |||
900.2.r.f.551.8 | 48 | 5.3 | odd | 4 | |||
900.2.r.f.551.16 | 48 | 20.3 | even | 4 | |||
900.2.r.f.851.8 | 48 | 180.23 | odd | 12 | |||
900.2.r.f.851.16 | 48 | 45.23 | even | 12 | |||
1620.2.e.b.971.1 | 48 | 45.7 | odd | 12 | |||
1620.2.e.b.971.2 | 48 | 180.47 | odd | 12 | |||
1620.2.e.b.971.47 | 48 | 180.7 | even | 12 | |||
1620.2.e.b.971.48 | 48 | 45.2 | even | 12 |